A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a ...In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.展开更多
For sustainable water resource management,it is important to determine the relationship between streamfl ow and other variables that infl uence availability of water resources.However,many catchments do not have suffi...For sustainable water resource management,it is important to determine the relationship between streamfl ow and other variables that infl uence availability of water resources.However,many catchments do not have suffi cient data to allow for a more detailed study of these relationships.We faced a similar challenge in the Chengcun Basin(limited historical data: from 1986–1999); and therefore we used a new approach to overcome this.We found that,using nonparametric trend methods in conjunction with the climate elasticity analyses and the 2D visualization of hydrologic data,it is possible to assess the relationships between streamfl ow and other hydro-climatic variables.In the past,streamfl ow trends in the basin were more correlated with precipitation than with potential evapotranspiration(PET).In addition,there is a gradual shift in the hydrological regime of the catchment,which may affect the occurrence of available water resources and activities that depend on them.In addition,based on our climate sensitivity analyses,the streamfl ow is dependent and more sensitive to variations in precipitation than to PET(δQ=0.79δP+0.42δE; precipitation elasticity,ε P=1.32; PET elasticity,ε E=-2.10).Therefore pending more detailed studies,the use of our approach will provide a rapid means to assess the variation of water resources(streamfl ow)in a watershed.In the future,we hope to carry out related research in other watersheds and also perform a more detailed studies to improve upon the results of this study.展开更多
The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group...The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.展开更多
Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triax...Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.展开更多
The aim of the present study was to assess spatial features of tuberculosis prevalence and their relationships with four main ethnic communities in Taiwan. Methods of spatial analysis were clustering pattern determina...The aim of the present study was to assess spatial features of tuberculosis prevalence and their relationships with four main ethnic communities in Taiwan. Methods of spatial analysis were clustering pattern determination (such as global version of Moran’s test and local version of Gi*(d) statistic), using logistic regression calculations to identify spatial distributions over a contiguous five years and identify significant similarities, discriminant analysis to classify variables, and geographically weighted regression (GWR) to determine the strength of relationships between tuberculosis prevalence and ethnic variables in spatial features. Tuberculosis demonstrated decreasing trends in prevalence in both genders during 2005 to 2009. All results of the global Moran’s tests indicated spatial heterogeneity and clusters in the plain and mountainous Aboriginal townships. The Gi*(d) statistic calculated z-score outcomes, categorized as clusters or non-clusters, at at 5% significance level. According to the stepwise Wilks’ lambda discriminant analysis, in the Aborigines and Hoklo communities townships with clusters of tuberculosis cases differentiated from townships without cluster cases, to a greater extent than in the other communities. In the GWR models, the explanatory variables demonstrated significant and positive signs of parameter estimates in clusters occurring in plain and mountainous aboriginal townships. The explanatory variables of both the Hoklo and Hakka communities demonstrated significant, but negative, signs of parameter estimates. The Mainlander community did not significantly associate with cluster patterns of tuberculosis in Taiwan. Results indicated that locations of high tuberculosis prevalence closely related to areas containing higher proportions of the Aboriginal community in Taiwan. This information is relevant for assessment of spatial risk factors, which, in turn, can facilitate the planning of the most advantageous types of health care policies, and implementation of effective health care services.展开更多
基金Supported by the Natural Science Foundation of Hubei Province!(992P0 30 7) the National Natural Science Foun-dation of Chi
文摘A simple method for solving Cauchy’s problem of wave equations in higher space dimensions with initial condition of separated variables, has been given by using D’Alembert’s formula and some examples have been shown.
文摘In this paper we study the solutions and stability of the generalized Wilson＇s functional equation fc f（xty）dtt（t） ＋ fc f（xtσ（y））dtt（t） =2f（x）g（y）, x,y C G, where G is a locally compact group, a is a continuous involution of G and # is an idempotent complex measure with compact support and which is a-invariant. We show that ∫Gg（xty）dp（t） ＋ fcg（xta（y））dp（t） = 2g（x）g（y） if f = 0 and fcf（t.）dp（t） =0, where [fcf（t.）dp（t）]（x） = fc f（tx）dμ（t）. We also study some stability theorems of that equation and we establish the stability on noncommutative groups of the classical Wilson＇s functional equation f（xy） ＋ X（y）f（xa（y）） = 2f（x）g（y） x, y C G, where X is a unitary character of G.
基金Supported by the Hohai University Scholarship Schemethe National Natural Science Foundation of China(Nos.41130639,51179045,41101017,412010208)the Innovation Program for Graduates in Jiangsu Province,China(No.CXZZ13_02)
文摘For sustainable water resource management,it is important to determine the relationship between streamfl ow and other variables that infl uence availability of water resources.However,many catchments do not have suffi cient data to allow for a more detailed study of these relationships.We faced a similar challenge in the Chengcun Basin(limited historical data: from 1986–1999); and therefore we used a new approach to overcome this.We found that,using nonparametric trend methods in conjunction with the climate elasticity analyses and the 2D visualization of hydrologic data,it is possible to assess the relationships between streamfl ow and other hydro-climatic variables.In the past,streamfl ow trends in the basin were more correlated with precipitation than with potential evapotranspiration(PET).In addition,there is a gradual shift in the hydrological regime of the catchment,which may affect the occurrence of available water resources and activities that depend on them.In addition,based on our climate sensitivity analyses,the streamfl ow is dependent and more sensitive to variations in precipitation than to PET(δQ=0.79δP+0.42δE; precipitation elasticity,ε P=1.32; PET elasticity,ε E=-2.10).Therefore pending more detailed studies,the use of our approach will provide a rapid means to assess the variation of water resources(streamfl ow)in a watershed.In the future,we hope to carry out related research in other watersheds and also perform a more detailed studies to improve upon the results of this study.
文摘The aim of this paper is to investigate the superstability problem for the pexiderized trigonometric functional equation∑ v∈Φ∫Kf（xkv（y）k^-1）dwK（k）= Φ g（x）h（y）, x, y ∈ G,where G is any topological group, K is a compact subgroup of G, ωK is the normalized Haar measure of K, Φ is a finite group of K-invariant morphisms of G and f, g, h are continuous complex-valued functions.Consequently, we have generalized the results of stability for d＇Alembert＇s and Wilson＇s equations by R. Badora, J. Baker, B. Bouikhalene, P. Gavruta, S. Kabbaj, Pl. Kannappan, G. H.Kim, J.M. Rassias, A. Roukbi, L. Sz′ekelyhidi, D. Zeglami, etc.
文摘Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.
文摘The aim of the present study was to assess spatial features of tuberculosis prevalence and their relationships with four main ethnic communities in Taiwan. Methods of spatial analysis were clustering pattern determination (such as global version of Moran’s test and local version of Gi*(d) statistic), using logistic regression calculations to identify spatial distributions over a contiguous five years and identify significant similarities, discriminant analysis to classify variables, and geographically weighted regression (GWR) to determine the strength of relationships between tuberculosis prevalence and ethnic variables in spatial features. Tuberculosis demonstrated decreasing trends in prevalence in both genders during 2005 to 2009. All results of the global Moran’s tests indicated spatial heterogeneity and clusters in the plain and mountainous Aboriginal townships. The Gi*(d) statistic calculated z-score outcomes, categorized as clusters or non-clusters, at at 5% significance level. According to the stepwise Wilks’ lambda discriminant analysis, in the Aborigines and Hoklo communities townships with clusters of tuberculosis cases differentiated from townships without cluster cases, to a greater extent than in the other communities. In the GWR models, the explanatory variables demonstrated significant and positive signs of parameter estimates in clusters occurring in plain and mountainous aboriginal townships. The explanatory variables of both the Hoklo and Hakka communities demonstrated significant, but negative, signs of parameter estimates. The Mainlander community did not significantly associate with cluster patterns of tuberculosis in Taiwan. Results indicated that locations of high tuberculosis prevalence closely related to areas containing higher proportions of the Aboriginal community in Taiwan. This information is relevant for assessment of spatial risk factors, which, in turn, can facilitate the planning of the most advantageous types of health care policies, and implementation of effective health care services.
